Prompt Gamma Enhancement with Nanoparticles
The tumor volume material (see Figure 1
) can be filled with water or a mixture of water with nanoparticles (Ag, Al, Au, Bi, Cd, Gd, Hf, Si or Ti). The nanoparticles (NPs) number is determined based on a 1% NP mass weight condition. This concentration is comparable to the gold concentration measured by Hainfeld et al. for in vivo tumors [30
]. The proton beam energy is set to 150 MeV. Figure 2
presents the energy deposited by the proton along its path.
As the “dense bone” density (1.575 g/cm3
) is higher than water (1.000 g/cm3
), a higher energy deposition is observed between a 9 and 11 cm depth. As expected, depending on the “tumor volume” composition, the energy deposited is affected and, consequently, the proton range. The lowest range is obtained in the case of an Au of 1% weight whereas the maximum range corresponds to the case of a water target (see Table 2
). Figure 3
shows the PG rays longitudinal distributions after 150 MeV proton irradiation.
The amount of PG emitted from Gd loaded tumor is the most significant. However, the majority of this signal is constituted by secondary PG resulting from (n,γ) reactions. Indeed, two gadolinium isotopes have a large capture cross section for thermal neutrons: 60,900 b for 155
Gd (isotopic abundance 14.80%) and 254,000 b for 175
Gd (isotopic abundance 15.65%) [33
]. Since the proton range information is linked to the primary gamma rays and not the secondary gamma, the amount of secondary gamma is not relevant for range estimation.
As is similar to the energy deposition profile, a decrease in the PG yield is observed in the adipose tissue region between a 5 and 7 cm depth and an important increase can be noted between a 9 and 11 cm depth in the dense bone area. This is partly due to the stopping power value differences between both materials and additional (p,γ) reactions that are produced in the bone area, e.g., 31
P, producing 1266 keV gamma or 40
Ca with deexcitation at 3736 keV [34
]. In addition, the PG ray profile is dependent on the composition of the “tumor volume”.
In order to evaluate the correlation between the PG signal intensity and the BP shifts, we calculated the particle beam range and the PG range for each material. The particle range corresponds to the position of the 80% BP distal fall off. Similarly, the PG range is the position corresponding to the 80% PG emission yield fall-off. The obtained results are presented in Table 2
. A significant Pearson’s correlation coefficient of 0.9993 (p
value < 0.01) was calculated between the two ranges. A normalized dose and associated total PG emission are presented for water and tumor loaded with SiNP in supplemental Figure S1
For each material, PG rays provide a high accuracy in order to estimate the proton beam range. The small 2 mm mismatch between the PG range and actual beam range is a known offset and results from the low proton energy at this depth, which is too low to drive nuclear reactions. Notably, the BP position slightly shifts to lower values when the metal atomic number increases, as expected from Bethe-Bloch formula.
In order to determine the optimal nanoparticle composition to enhance PG emission, for each nanoparticle material, the ratio between the primary gamma yield at 80% PG fall off and the secondary gamma yield at 80% PG is calculated and compared to that obtained for water alone. The results are presented in Table 3
Among the tested metals, the maximum absolute yield for primary PG rays emission was obtained for AgNP. However, the presence of Ag, Au, Cd, Gd, Hf, and Ti nanoparticles lead to a decrease in the primary to secondary PG ratio when compared to water. The proton range information is linked to the primary gamma rays and the secondary gamma rays could lead to significant interference on the BP tracking. Therefore, the best choice corresponds to the one that maximizes the primary PG emission yield compared to the secondary PG emission yield. From Table 3
, it can be observed that AlNP, BiNP and SiNP are the best suited. The ratio between primary and secondary PG yield is increased by 6%, 3% and 3% for SiNP, AlNP and BiNP, respectively, compared to water. Among these, the maximum absolute yield for primary PG ray emission is obtained for BiNP. The presence of Ag, Au, Cd, Gd, Hf, and Ti nanoparticles leads to a decrease in the primary to secondary PG ratio when comparing to water. If we assume a 2 Gy dose deposition (typical value of dose per fraction in daily radiotherapy sessions) delivered as pristine peaks, this corresponds to 1.68 × 1011
protons passing through the tumor volume in our configuration. This means that the presence of 1% Si NP in the tumor volume leads to 8 × 106
additional primary PG compared to the water control.
Some particular spectroscopic features were found in the energy spectra. Figure 4
shows the total gamma energy spectra and the primary PG energy spectra after 150 MeV proton irradiation between 1 and 8 MeV. Figure S2
can be referred to as a reference for the gamma rays emitted in the 0–1 MeV range. Most of the peaks originate from spallation reactions, neutron capture or inelastic proton interactions. It should be noted that, as the tumor volume is a mixture of water +1% weight of metallic nanoparticles, all characteristic peaks for water were also present with the same intensities. Common PG peaks for water and peaks of interest for silicon are presented in Table 4
. Most reactions are listed in [34
For proton-induced reactions, a comparison between Figure 4
a,b and c,d highlights that the most prominent PG emission peaks originates from secondary processes such (n,γ) nuclear reactions. The interactions of the proton beam within the patient inevitably lead to neutron production, that in turn generate secondary nuclear reactions, resulting in an unintended dose. For instance, the 2.23 MeV peak results from neutron capture by hydrogen nuclei, namely 1
Cd has a very high cross section for thermal neutron capture (~20,600 b), giving rise to numerous peaks below 1 MeV (cfr. Figure S2
) and two intense higher energy peaks at 4.44 and 4.79 MeV [37
Gd also produced an intense peak at 7.937 MeV [33
]. Other prominent rays can be identified at 6.512, 6.81, 7.28, and 7.63 MeV after the bombardment of 197
Ag and 177
Hf, respectively. The relative importance of secondary processes when investigating the proton range through NP use can also be observed by analyzing Table 3
. Ratios that are much smaller than the water equivalent value represent pollution in the PG signal and to additional doses in the patient, discarding Gd and Cd NP, and, to a lesser degree, Hf NP.
A closer look at Figure 4
c,d highlights an interesting emission peak found for SiNP at 1.779 MeV. Figure 5
presents the fold change with respect to water of primary PG from the tumor volume loaded with 1%wt SiNP or 1% wt AlNP. The 1.779 MeV PG emission peak on Figure 5
a originates from the proton interaction through the 28
P* process. However, another competing reaction, 28
Al*, produces radioactive aluminum nuclides that relax at an identical energy. For cross sections of approximately the same order of magnitude, it may be difficult to precisely estimate the contribution of the (p,nγ) reaction that relates to the proton beam position [34
]. A low energy PG emission peak at 1.014 MeV was observed for both SiNP and AlNP with similar intensities, resulting from 28
Al* and 27
Al* reactions (Figure 5
a,b). In the case of AlNP, the 27
Mg* reaction gave rise to the 1.809 MeV peak, contributing to the PG signal, although to a lesser extent. No identifiable peak was observed in the case of BiNPs.